First-time visitors to New York can't see and do everything, and you shouldn't try. You can, however, get a wonderful introduction to the sights, visit famous attractions, and make notes for a return visit.
Day 1
A double-decker bus tour is a good way to get oriented. Tours let you get off at top attractions and reboard a later bus to continue your exploration.
Visit the Statue of Liberty or simply view it from the water on a cruise or from the free Staten Island ferry. However you do it, seeing the city from the water is unforgettable. The Ellis Island Immigration Museum, near the Statue of Liberty, conveys the experiences of the forebears of nearly one in four Americans.
While in the downtown area, explore the South Street Seaport, which has many restaurants and shops on the water and beautiful views of the Brooklyn Bridge.
The evening may be spent wandering through SoHo with its stylish art galleries, boutiques, and bistros housed in historic cast iron buildings among cobblestone streets or soaking up the student and artist atmosphere in Greenwich Village. See Stanford White's Washington Arch at the Fifth Avenue side of Washington Square Park.
Day 2
For another full day, spend the morning in Midtown East. Admire the Art Deco Chrysler Building and visit the United Nations. Take a free tour (Wednesdays) of the newly restored Grand Central Terminal and lunch in one of its restaurants under the famous sky ceiling.
In the afternoon, walk a few cross-town blocks to Rockefeller Center. See the Channel Gardens, statue of Prometheus, and the Lower Plaza which is especially spectacular in winter when the giant Christmas tree is lit and the ice rink is full. In warmer weather, the Lower Plaza becomes an outdoor restaurant. Walk up Fifth Avenue past St. Patrick's Cathedral, Trump Tower, and countless upscale stores. Stroll west to Radio City Music Hall or north to The Museum of Modern Art (MoMA).
End your day with a memorable performance at Lincoln Center, home of the Metropolitan Opera, New York Philharmonic, Jazz at Lincoln Center, New York City Opera, and New York City Ballet.
Day 3
On your third day, stroll (or join a bike tour operated by Central Park Bicycle Tours) through Central Park. At 82nd Street and the park is the Metropolitan Museum of Art. Among the 150 wonderful museums in New York City, the Met - the largest museum in the Western Hemisphere -covers 5,000 years of cultural history.
Take the bus down Fifth Avenue to 59th Street. The ride takes you past magnificent, mostly residential, buildings. Then walk down Fifth, with its great shopping, and head west to Times Square, the brightest symbol of New York's revitalization. Buy a discount ticket for a Broadway show playing that evening at the TKTS booth at Broadway and 47th Street.
Before your show, ride to the 86th-floor outdoor observatory of the Empire State Building. If you go late in the afternoon, you'll see the city by day and by evening, all lit up. Eat at a theater district restaurant; many have pre-theater dinner specials.